First thing I would do is change the spark plug and the filter. It needs to be serviced just like a car. Yearly maintenance should take care of any problems. One thing we do is, at the end of the season drain out all the gas, so water does not accumulatein the tank. Always refer to your manual.
Gasoline engines require both fuel and spark in order to operate. Since the mower has fuel the next area of concern is the spark. Try removing the spark plug cleaning the hole with a pipe cleaner. Take the old plug to a hardware store and purchase an identical plug. Reinsert the plug and fire it up!
I had a problem with my lawn mower not starting once. It would start, then die quickly. I changed the spark plug first. Still did the same thing. Finally I took it down and had it tested and while it was there the tech primed the mower, then tried starting it, he primed again and it stayed running
First check your spark plug to make sure that the tip is not black w/carbon, if so replace it. Then check the air-filter for any blockage and replace if needed. Lastly, check the fuel line to see if it is blocked or leaking fuel. Most likely cause: bad sparkplug.
Could be one of several things: plugged fuel line, bad spark plug or plug wire, or, especially if the mower has sat for a while with fuel in it, varnish in the carburetor. Check all three; it'll be one of these 99% of the time.